Problem: Simplify the following expression: $ y = \dfrac{-2q - 8}{10} - \dfrac{3}{7} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-2q - 8}{10} \times \dfrac{7}{7} = \dfrac{-14q - 56}{70} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{3}{7} \times \dfrac{10}{10} = \dfrac{30}{70} $ Therefore $ y = \dfrac{-14q - 56}{70} - \dfrac{30}{70} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{-14q - 56 - 30 }{70} $ Distribute the negative sign: $y = \dfrac{-14q - 56 - 30}{70}$ $y = \dfrac{-14q - 86}{70}$ Simplify the expression by dividing the numerator and denominator by 2: $y = \dfrac{-7q - 43}{35}$